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X>0 (sin[x])/x 
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#1
Mar1911, 05:20 AM

P: 131

does lim _{x>0} (sin[x])/x exist ? if yes then what is it , iguess 0 , but cannot figure out the reason .. pl. help...
note: [x] is greatest integer less than or equal to x 


#2
Mar1911, 06:21 AM

Sci Advisor
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Thanks
P: 26,157

hi phymatter!
(just choose your delta to be 0.9, whatever your epsilon ) 


#3
Mar1911, 03:37 PM

Sci Advisor
P: 6,039

If1 < x < 0, [x] = 1, if 0 < x < 1, [x] = 0. As a result , for x < 0, the limit is ∞ while for x > 0, the limit is 0.



#4
Mar1911, 05:40 PM

P: 737

X>0 (sin[x])/x
I don't think it would exist. lim(x>0+) sin(floor(x))/x = 0 and lim(x>0) sin(floor(x))/x = ∞. For there to be a limit, lim(x>0+) sin(floor(x))/x and lim(x>0) sin(floor(x))/x must be equal, they're not. 


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